some of the graph energies of zero-divisor graphs of finite commutative rings

In this paper, we investigate some of the graph energies of the zero-divisor graph γ(r) of finite commutative rings r. let z(r) be the set of zero-divisors of a commutative ring r with non-zero identity and z∗(r) = z(r) {0}. the zero-divisor graph of r, denoted by γ(r), is a simple graph whose vertex set in z∗(r) and two vertices u and v are adjacent if and only if uv = vu = 0. we investigate some energies of γ(r) for the commutative rings r ≃ zp2 × zq, r ≃ zp × zp × zp and r ≃ zp × zp × zp × zp where p, q the prime numbers.